Promising impact of push–pull configuration into designed octacyclic naphthalene-based organic scaffolds for nonlinear optical amplitudes: a quantum chemical approach

In opto-electronics, non-fullerene (NF) derivatives are regarded as efficient non-linear optical (NLO) materials. The present investigation was based on designing NF naphthalene-based derivatives (PCMD1–D9) with D-π-A configuration from PCMR. DFT analysis at M06/6-311G (d,p) level was accomplished to explore the photonic behavior of PCMD1–D9 compounds. Various kind of analysis like; UV–Vis, density of state (DOS), natural bond orbitals (NBOs), transition density matrix (TDM) and frontier molecular orbitals (FMOs) analyses were accomplished to understand the NLO properties of said chromophores. The configuration change led to considerable charge distribution over highest occupied and lowest unoccupied molecular orbitals with minimum band difference. The energy gap trend for all the entitled compounds was observed as; PCMD8 < PCMD5 = PCMD9 < PCMD6 < PCMD7 < PCMD4 < PCMD3 < PCMD2 < PCMD1 with the least band gap of 2.048 eV in PCMD8 among all the compounds. The UV–Visible spectrum of the entitled chromophores manifested high values of λmax in derivatives contrary to PCMR. Additionally, NBO findings explored effective intramolecular charge transfer and maximum energy of stabilization (34.31 kcal/mol) for PCMD8 chromophore. The highest linear polarizability () and dipole moment (µtot) values were exhibited by PCMD5 at 2.712 × 10–22. and 1.995 × 10–17 esu, respectively. PCMD8 push–pull configured molecular entity exhibited highest first hyper-polarizability (βtot) at 4.747 × 10–27 esu and second hyper-polarizability at 6.867 × 10–32 esu. Overall, all the formulated chromophores exhibited significant NLO results contrary to PCMR. Hence, through this structural tailoring via various acceptors, effective NLO materials were obtained for optoelectronic applications.


Electronic structures
NLO characteristics of molecule's electronic structure is determine by frontier molecular investigation 37 .Light absorption molecular capability, electronic properties and chemical stability are comprehended via FMO analysis 30,38,39 .Highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energy gap is directly influenced by above mentioned factors.These orbitals determine intra-molecular charge transference efficiency [40][41][42] .However, their energy difference (ΔE) is efficient to know molecular chemical reactivity as well as dynamic stability Less ΔE value corresponds to high polarizability which in turn lead to exceptional NLO behavior 43 .On the other hand, high ΔE value corresponds to molecular stability and hardness leading to less reactivity and chemical alteration.Table 1 displays energy difference along with energy values of HOMO and LUMO for the designed organic compounds.
From the above table, the reference organic molecule (PCMR) possesses − 5.941 and − 3.505 eV of HOMO and LUMO energies, which are comparable to the experimental values of − 5.75 and − 4.15 eV, respectively, indicating the accurateness in the selection of functional group for the present analysis.The achieved values of HOMO for all the derivatives (PCMD1-D9) are higher than the reference compound at − 5.658, − 5.637, − 5.649, − 5.657, − 5.69 7, − 5.682, − 5.659, − 5.696 and − 5.693 eV, respectively.However, the obtained LUMO values for PCMD1-D4 and PCMD7 are higher than the reference i.e., − 3.362, − 3.352, − 3.402, − 3.445 and − 3.459 eV, correspondingly but on the other hand PCMD5, PCMD6, PCMD8 and PCMD9 exhibit less values than PCMR at − 3.623, − 3.525, 3.648 and − 3.619 eV, respectively.Hence, the high HOMO and less LUMO values result in less band gap in PCMD5, PCMD6, PCMD8 and PCMD9 showing high charge transmission probability in these molecules.
The highest band gap is exhibited by PCMR at 2.436 eV.This largest energy difference is attributed to the presence of 2-(5,6-difluoro-3-oxo-2,3-dihydro-1H-inden-1-ylidene)malononitrile as a acceptor motifs with A-π-A configuration.Because moving from PCMR to PCMD1 the one end capped acceptor group is substituted with 9-phenyl-9H-carbazole which significantly reduces the band gap to 2.296 eV in PCMD1.
Conversely, the least band gap value of 2.048 eV is present in PCMD8, that might be owing to the presence of high electronegative nitro functional groups at 6 and 7 positioning of 1-(dicyanomethylene)-3-oxo-2,3-dihydro-1H-cyclopenta[b]naphthalene (DMP) acceptor group.The second lowest energy gap value is exhibited by PCMD5 and PCMD9 at 2.074 eV because of the presence of sulfonic acid groups and cyano groups at 6 and 7 positioning of DMP acceptor moiety rendering high electron withdrawing tendency.However, PCMD6 possess 2.157 eV energy gap resulted from the 6, 7 positioning of trifluoromethyl functional group in DMP.The presence of acetate, chloro and fluoro groups at 6, 7 positioning of DMP acceptor group in PCMD7, PCMD4 and PCMD3 corresponds to band gap of 2.200, 2.212 and 2.247 eV, respectively.2.285 eV of energy gap is present in PCMD2 in relation to the absence of any electron withdrawing functional groups in DMP.The ascending order of energy difference (HOMO/LUMO) for the derivatives is PCMD8 < PCMD5 = PCMD9 < PCMD6 < PCMD7 < PCMD4 < PCMD3 < PCMD2 < PCMD1.Figure 3  complete electronic transmission from HOMO of donor and π-spacer groups towards acceptor.Concluding our discussion, the less energy difference as exhibited by formulated derivatives, which supported the grater absorption properties that indicates their high efficiency in modern optical devices.

Density of states (DOS)
The DOS analysis verify the results shown by the FMOs diagrams and explain the electronic distribution in frontier molecular orbitals 44 .In DOS pictographs, the HOMO signifies valence band showing negative values while the positive values are represented by the conduction band (LUMO) 45 .The analysis was performed at the same DFT functional for PCMR and PCMD1-D9.DOS indicates the contribution of each fragment of molecule in charge transfer.For determining the density of states (DOS), we split our studied molecules into se98parate fragments.The PCMR1 was divided into two fragments i.e., donor (D) and acceptor (A) while, the derivatives (PCMD1-D9) were divided into three segments i.e., donor, π-spacer, and acceptor.From Fig. 4, it is demonstrated that in PCMR molecule HOMO density appear on donor unit while LUMO density is majorly present on acceptor units.In the designed molecules PCMD1-D9, distribution pattern of HOMO and LUMO density is same as HOMO density is majorly placed on π-spacer while minor HOMO density is situated on donor atoms.LUMO  The percentages of electronic cloud distribution molecular orbitals is same as illustrated in FMOs surfaces.The overall contribution pattern has shown a significant electronic charge variation in molecular systems, which depicts that a considerable amount of charge transfer takes place from the donor to acceptor region via the π-spacer.

Absorption spectrum
The ultraviolet visible computation in gaseous form for PCMR and PCMD1-D9 were performed at M06/6-311G(d,p) to apprehend oscillator strength as well as excitation energy with relation to important electronic transitions 46,47 .Franck-Condon principle relates spectral highest absorption maxima (λ max ) to vertical excitation.The information about oscillator strength (f os ), absorption maxima (λ max ), excitation energy (E), along with molecular orbital (MO) contribution in transition are given in Table S12 (rest of data is given in Table S11).The spectral representation of absorption maxima (λ max ) in ultraviolet visible region for PCMR and PCMD1-D9 is presented in Fig. 5.
From the major findings presented in Table S12, the absorption maxima (λ max ) value for reference (PCMR) i.e., 606.899 nm is lowest among all the compounds with transition energy of 2.043 eV, 2.956 oscillator strength and molecular orbital contribution from HOMO to LUMO of 95%, however, from HOMO-1 to LUMO-1 it is 3%.Hence, it is observed that absorption maxima are significantly impacted by highly electron rich donor and electron withdrawing acceptor end capped groups as well as molecular configuration (reference (A-π-A)→ derivatives (D-π-A)) creating strong push pull mechanism.The least λ max value of reference compound resulted from two electron withdrawing acceptor groups on either side of the π-linker.However, the highest λ max value of 701.541 nm is exhibited by PCMD8 among all the chromophores because of high electronegative nitro functional groups present in DMP acceptor group, results in 1.767 eV energy of transition and oscillator strength of 1.299.The molecular orbital contribution exhibited by PCMD8 compound is 96% from HOMO to LUMO and 3% HOMO-1 to LUMO.The second highest λ max of 696.849 nm is present in PCMD5 due to the presence of sulfonic acid groups in DMP with 1.779 eV of transition energy, 1.779 f os and MO contribution of 95 and 3% from HOMO to LUMO and HOMO-1 to LUMO, respectively.However, the third highest λ max of 695.442 nm is shown by PCMD9 because of cyano groups presence in DMP with transition energy and f os values of 1.783 eV and 1.362, respectively.However, the molecular orbital contributions in PCMD9 corresponds to 95% from HOMO to LUMO and 3% from HOMO-1 to LUMO.Owing to the presence of trifluoromethyl groups in PCMD6, the λ max reduces to 663.580 nm with E 1.868 eV, 1.504 f os and MO contributions of 95 and 3% from HOMO to LUMO and HOMO-1 to LUMO, respectively.Substituting trifluoromethyl groups by chloro groups result in λ max of 641.238 nm in PCMD4 with E 1.934 eV, 1.687 f os and MO contributions of 95 and 3% from HOMO to LUMO and HOMO-1 to LUMO, respectively.The overall decreasing trend for PCMD1-D9 as; PCMD8 > PCM D5 > PCMD9 > PCMD6 > PCMD4 > > PCMD3 > PCMD1 > PCMD2 with chief molecular orbital contribution is from HOMO to LUMO of 94-96%.The compounds with lower E g showed wider absorption spectrum as the decreasing trend of λ max is almost similar with the increasing trend of energy gap.All fabricated molecules showed bathochromic shift (Fig. 5) with reduced band gap than that of reference molecule, particularly, PCMD8.Hence, it is anticipated that these chromophores will be significantly utilized for NLO materials.www.nature.com/scientificreports/

Natural bond orbitals (NBO)
To study charge density migration and hyper conjugation resulting from non-covalent interactions between acceptor and donor groups, natural bond orbitals investigation is employed.Equation ( 12) was applied to calculate energy of stabilization.www.nature.com/scientificreports/ Here, q i corresponds to donor orbital occupancy, E i and E j denotes off-diagonal NBO Fock or Kohn-Sham medium elements, whereas the diagonal is characterized by F(i.j) 48,49 .σ → σ*, π → π*, LP → σ* and LP → π* orbital ( 12)

Global reactivity descriptors
Global reactivity parameters (GRPs) encompass multiple descriptors i.e. global softness (σ), chemical potential (μ) 32 , ionization potential (IP) 33 , electronegativity (X) 34 , global hardness (η) 35 , electron affinity (EA) and global electrophilicity index (ω) 36 that impart knowledge about molecular stability and its reactivity.Ionization potential (IP) is the principal parameter which defines energy needed to eliminate electron out of MO.From Table 3, highest energy of ionization potential of 5.94 eV is demonstrated by PCMD9 manifesting efficient electron contribution by donor group towards the acceptor part.While the least IP value is present in PCMD1 i.e. 5.64 eV.The trend for IP value is; PCMD9 > PCMD4 = PCMD7 > PCMD8 > PCMD5 > PCMD3 = PCMR > PCMD2 > PC MD1.Conversely, energy liberates on electronic insertion in valence shell is termed as electron affinity (EA).The highest EA is exhibited by PCMD7 at 3.65 eV while 3.35 eV is the least energy released upon electronic addition in PCMD1.Knowledge about polarization of electronic cloud is collected from global softness (σ) and global hardness (η) values.High polarization of electronic cloud is demonstrated by softer molecules while Vol:.(1234567890

Transition density matrix
Transition density matrices (TDMs) is employed for visualizing and investigating optical nature of each electronic transition in a molecular system during excited state charge dispersion and electron-hole mobility 50 .Attaining transition density is the principal cause of TDMs inquiry.Off diagonal elements of transition density matrix manifest various basis function couplings during electronic transition.These varied basis functions (correspondent to diverse atomic centers) demonstrate density of transition which is the estimation of excitations involving charge transmission.Whereas, local excitations corresponds to transition density demonstrated by equivalent basis functions (correspondent to same atomic centers) 51 .
The current inquiry of PCMR and PCMD1-D9 has been executed at M06/6-311G(d,p) via Multiwfn 3.7 (Fig. 6).The formulated compounds (PCMD1-D9) have been categorized into D, π-bridge and A, however the reference is distributed into two acceptors and a π-bridge.In reference compound, the density is mainly localized over donor with minor transmission over acceptor groups.The bright points in the TDMs graphs manifests charge localization on donor group with very minute disposition on acceptor indicating less charge transmission towards acceptor in the case of reference compound.However, in the case of derivatives the major dispersion of charge density is over π-bridge and acceptor as indicated by bright points with almost no density localization over donor group.This shows efficient charge density transmission from donor to π-bridge and then towards acceptor in the derivatives.Therefore, transitions in derivatives are charge transmission excitations accompanied by considerable charge consistency in off-diagonal along with diagonal elements.

Nonlinear optical activity
NLO is an eminent discipline of current investigations due to its importance in managing primary tasks of optical memory, telecommunications, signal processing, frequency shifting, optical interconnections, optical logic, optical switching and optical modulation [52][53][54] .Hyperpolarizability and ICT describes the correlation between nonlinearity and molecular structure.Molecular high polarizability, dipole moment as well as hyperpolarizability corresponds to enhanced/large NLO behavior.The electric field strength that deforms electronic dissemination throughout the compound is termed as linear polarizability (α).While atomic and molecular nonlinearity subject to extensive nonlinear optical phenomenon is hyperpolarizability (β, γ, etc.).The first order hyperpolarizability (β tot ), second order hyperpolarizability (γ tot ), linear polarizability (<α>) and dipole moment (µ tot ) values including tensors for PCMR and PCMD1-D9 are presented in Tables S23-S26 and Table 4.
The dipole polarizability (µ) is greatly affected by difference of electronegativity that could be categorically the product of charge magnitude and distance among them, where high electronegativity corresponds to large µ 55 .Besides, molecular µ, polarity is crucial in improving molecular nonlinearity.The µ tot characterize average dipole moment, whereas, tensors contributes to µ tot along x, y and z-orientations are µ x , µ y and µ z 56  µ tot (Table S22).The PCMD5 chromophore having highest µ tot of 1.995 × 10 -17 esu with µ x = 1.953 × 10 -17 esu, µ y = 3.734 × 10 -18 esu and µ z = 1.561 × 10 -18 esu contribution by tensors possess highest polarizability.Specifically, for the comparison with para Nitroaniline (pNA) 57 , a standard molecule for investigating the NLO properties, these compounds exhibit 0.06, 0.23, 0.20, 0.22, 0.24, 0.40, 0.29, 0.24, and 0.37 times greater µ values.Similarly, when compared to CPTR1 58 , similar analog to our compounds, 0.8, 3.0, 2.6, 3.0, 3.2, 5.4, 3.8, 3.2, and 5.0 the times greater values are found in our fabricated chromophores.Table S22 indicates linear polarizability (<α>) values of PCMR and PCMD1-D9 along with polarizability contributing tensors and their values.The <α> value of 2.712 × 10 -22 esu is the highest polarizability value among all the chromophores exhibited by PCMD5.However, the least <α> value of 2.310 × 10  S24 contains comprehensive findings of hyperpolarizability, whereas the average hyperpolarizability (β tot ) values are tabulated in Table 4.The β tot highest of 4.747 × 10 -27 esu is exhibited by PCMD8, whereas the least hyperpolarizability is present in PCMR at 0.099 × 10 -27 esu.The same trend for second hyperpolarizability values has been observed, where the highest γ tot of 6.867 × 10 -32 esu is exhibited by PCMD8, but the least γ tot is present in PCMD1 at 3.517 × 10 -32 esu.Where the major contribution towards β tot is exhibited by β xxx tensor and γ tot in is by γ x tensor.Comparative analysis with pNA and CPTR1 our compounds illustrated higher values for β and γ tot 50 .In conclusion, the changing configuration from A-D-A to D-π-A and variant acceptor groups indicates substantial ICT besides bathochromic shift which in turn enhances the optical nonlinearity in all the designed chromophores.The high values of hyperpolarizability and polarizability manifest designed compounds as potential candidate for technologically advanced optical devices.

Conclusion
In current report, we devised novel octacyclic naphthalene-based PCMD1-D9 nonlinear organic compounds by substituting one end acceptor moiety in PCMR with donor (9-phenyl-9H-carbazole) in derivatives and altering acceptor group in each successive derivative.Quantum chemical calculation were applied to investigate the NLO behavior of fabricated chromophores.The NBO study revealed a hyper conjugative interaction played significant role in stabilizing the molecule.An efficient charge transference from donor to acceptor through spacer has been studied by FMO findings which were further also supported by DOS and TDM analysis.A lower band gap (2.048 eV) with greater red shift (701.541nm) is examined in PCMD8 than that of other molecules.From all the devised NLO compounds, PCMD8 demonstrated relatively high first hyperpolarizability and second hyperpolarizability of 4.747 × 10 -27 esu and 6.867 × 10 -32 esu, respectively.Nevertheless, PCMD5 manifested high dipole moment and linear polarizability value of 1.995 × 10 -17 esu and 2.712 × 10 -22 esu, respectively.So, PCMD8 and PCMD5 possessed high optoelectronic (linear and nonlinear) behavior resulted from the induction of nitro and sulfonic acid groups in the acceptor moiety.However, all the formulated compounds have shown higher nonlinearity on comparison with pNA as a standard molecule from the literature.Subsequently, PCMD8 chromophores is approved to be proficient NLO candidates for technologically advanced nonlinear optical devices.

Figure 4 .
Figure 4. Density of states diagrams of PCMR and PCMD1-D9 at M06/6-311G(d,p) level.Figures were drawn by utilizing PyMOlyze 1.1 version and output files were calculated through Gaussian 09 version D.01.
density in all the designed molecules is majorly present on acceptor units whereas minor amount is spread on donor atoms.In LUMO, the donor core percentage contribution for reference PCMR and designed molecules PCMD1-D9 are noted as 38.2, 0.2, 0.2, 0.2, 0.2, 0.1, 0.2, 0.2, 0.1 and 0.2% respectively which are correlated with FMOs surfaces.

Table 1 .
Energy difference between highest occupied and lowest unoccupied molecular orbitals along with their energy values for PCMR and PCMD1-D9 (in eV).
Vol.:(0123456789) Scientific Reports | (2023) 13:20104 | https://doi.org/10.1038/s41598-023-44327-9 least is associated with harder compounds.The highest η value is present in PCMD9 at 1.22 eV that reduces to 1.02 eV in PCMD7.The values of global softness (σ) are lesser than their respective global hardness (η) and global electrophilicity index (ω) values.PCMD7 manifests highest softness at 4.88 eV −1 with 0.436 eV −1 being the least softness among all compounds present in PCMD1.Hence all the fabricated chromophores exhibited the higher value of softness which supported the greater charge transference in them than reference chromophore which in result would express good NLO response.The highest value of global electrophilicity index (ω) is possessed by PCMD4 at 10.47 eV.While the lowest of 8.86 eV is present in PCMR.Chemical potential (μ) is inversely related to Electronegativity (X) value.Where, chemical potential describes affinity of electron removal while electronegativity reveals affinity to accept electrons.PCMD9 with highest electronegativity and lowest chemical potential at 4.72 and − 4.72 eV, correspondingly, manifests highest electron transmission in turn possess highest nonlinearity.

Table 2 .
Different transition types along with their values for PCMR and PCMD1-D9.